SOLUTION: please help: 6x-4y<-12 Graph the linear inequality

Question 161960: please help: 6x-4y<-12 Graph the linear inequality
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line

graph of

Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point

Substitute (0,0) into the inequality

Plug in and

Simplify

Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line. In other words, simply shade the ENTIRE region above the line.

Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

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